Mathematical description of the mechanical behaviour of metallic materials under creep conditions

The metallic materials creep behaviour has been described and a complete model is presented. The basic constitutive equation, as well as the structure parameters, have been derived from a mathematical analysis that represents the dominant physical procedures and mechanisms. The model is very general because it is referred to all stages of creep and describes the creep behaviour of all metallic materials, including those strengthened by a dispersion of second-phase particles. A creep function has been derived from the constitutive equation describing all three stages of creep under constant loading. The function has the minimum possible number of fitting, parameters. The dependence of the fitting parameters on the loading conditions has been described using very simple mathematical relations. Applications and predictions have been carried out in a wide range of metallic materials. Good agreement has been shown by a comparison made also between the creep curves determined experimentally, and those obtained from creep function and determined fitting parameters.     

Influence of voids on the stress distribution and deformation behaviour of epoxies under uniaxial deformation

A zero-order model is presented, which allows calculation of the stress distribution in porous epoxies by taking into account the interaction between randomly distributed voids. These results demonstrate that the mean value of the stress concentration factor increases with the volume fraction of voids. This leads to a decrease in sample yield strength. However, the generation of a porous morphology also creates a considerable number of regions where the stress is completely released. The theoretical predictions are in good agreement with experimental results obtained with macroporous epoxies, which were prepared based on the chemically induced phase separation technique, and tested under uniaxial compression.     

Numerical modeling of creep and creep damage in thin plates of arbitrary shape from materials with different behavior in tension and compression under plane stress conditions

A constitutive model for describing the creep and creep damage in initially isotropic materials with characteristics dependent on the loading type, such as tension, compression and shear, has been applied to the numerical modeling of creep deformation and creep damage growth in thin plates under plane stress conditions. The variational approach of establishing the basic equations of the plane stress problem under consideration has been introduced. For the solution of two‐dimensional creep problems, the fourth‐order Runge–Kutta–Merson's method of time integration, combined with the Ritz method and R‐functions theory, has been used. Numerical solutions to various problems have been obtained, and the processes of creep deformation and creep damage growth in thin plates of arbitrary shape have been investigated. The influence of tension–compression asymmetry on the stress–strain state and damage evolution, with time, in thin plates of arbitrary shape, has been discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

Modeling of creep deformation and its effect on stress distribution in multilayer systems under residual stress and external bending

A general theoretical model was developed to predict the creep deformation and its effect on the stress relaxation and distribution in the multilayer systems under residual stress and external bending. Based on the proposed solution, a simplified solution for the special case of one film layer on a substrate is also presented. Finite element analysis was carried out to validate the presented model. Good agreements were observed between the finite element simulation and the prediction of the proposed model. In addition, the effects of film thickness on creep strain and stress distribution, the creep effect on neural axis location in the bilayer assembly subjected to the combination of residual stress and external bending were also discussed.     

Moisture influence on the resilient deformation behaviour of unbound granular materials

The influence of moisture on the resilient deformation properties of unbound granular materials was investigated based on repeated load triaxial tests. Results showed that the resilient modulus (M_R) decreased with increasing moisture for a relatively low number of load cycles (N) where the deformation behaviour was mostly resilient with a negligible amount of associated accumulated permanent deformation (PD). Modelling attempts on this behaviour were quite satisfactory. Furthermore, the M_R showed an increasing trend with increasing moisture, up to the optimum, when the N was relatively large with a significant amount of accumulated PD. Above the optimum, the M_R generally decreased. Further investigation suggested that moisture aided the post-compaction (PC) and possible particle rearrangement that resulted in the increased PD and increased M_R. The existing model did not work in this case indicating that the effect of PC on M_R should be considered in modelling.     

Determination of tensile and compressive creep behaviour of ceramic materials from bend tests

We have developed equations that permit the determination of individual compressive and tensile creep rates from four-point bend test measurements made on trapezoidal bars. The equations developed are for the general stress dependence case. Finnie first proposed this type of analysis and solved the equations for the case of linear stress dependence. We present graphs that show solutions to the equations for the stress squared case. Creep measurements were performed on trapezoidal HS-130 Si₃ N ₄ bars to determine the ratio of compressive to tensile creep (). The values determined on four separate tests using two different temperatures and beam dimension ratios b ₂/b ₁ gave fairly consistent results. The s for previously unstrained material are: 0.24, 0.14, 0.17, and 0.17 with the average value of =0.18. For the case of prestrained Si₃N₄, is 0.48. To further test the usefulness of this analysis, data from a conventional (rectangular bars) four-point bend test were taken from the literature and analysed using the equations developed in this paper and the average determined value of . The individual tensile and compressive creep rates determined in this manner were found to agree very closely with other literature data measured in direct tension and compression tests.The experimental work was performed at the Metallurgy and Ceramics Laboratory, Aerospace Research Laboratories (AFSC), Wright-Patterson AFB, Ohio, USA.     

The deformation and fracture behavior of an electrodeposited nanocrystalline Ni under compression

A bulk and dense nanocrystalline Ni with an average grain size of 19 nm and a thickness of 5.4 mm was fabricated by an electro-deposition technique. The nc Ni had a preferable (2 0 0) growth texture along the depositing direction. Under compression test, the nc Ni exhibited a high strength of 2920 MPa and an accepted good ductility of 16%. A novel fracture character, i.e., the triple-junction shaped micro-cracks with the size varying from few to several tens of micrometers which run through the holistic fracture body of the nc Ni, was observed. The reason for the formation of such cracks is attributed to GB activities, which leads to the formation of nano-sized void, and the subsequent formation of micro-crack.     

The compression creep behaviour of silicon nitride ceramics

A comparison has been made of the compression creep characteristics of samples of reaction-bonded and hot-pressed silicon nitride, a sialon and silicon carbide. In addition, the effects of factors such as oxide additions and fabrication variables on the creep resistance of reaction-bonded material and the influence of dispersions of SiC particles on the creep properties of hot-pressed silicon nitride have been considered. For the entire range of materials examined, the creep behaviour appears to be determined primarily by the rate at which the development of grain boundary microcracks allows relative movement of the crystals to take place. Now with the BNF Metals Technology Centre, Wantage.     

Material deformation and fracture under impulsive loading conditions

Engineering structures experience impulsive loads during the time of natural disasters like earthquakes, cyclones and collisions. The design of structures resistant to such natural disasters requires an understanding of the deformation and fracture behaviour of the materials constituting the structure under impulsive loading conditions. In this paper the various aspects of dynamic plastic deformation and fracture of common engineering materials are reviewed and contrasted with their behaviour under static loading conditions.     

The creep and fracture behaviour of tempered martensitic steels

Creep strength enhanced ferritic steels contain 9 to 12% Cr and were developed to exhibit excellent high temperature properties. These should be achieved when the microstructure exhibits a tempered martensitic matrix containing a substructure with a high dislocation density and a uniform dispersion of fine, second phase precipitates. It is interesting to note that when properly processed the typical alloy compositions for these steels provide reasonable strength but can exhibit brittle creep behaviour. The levels of ductility required in engineering applications necessitate proper control of composition (including trace elements), steel making and processing and all heat treatments. The properties needed for modern design methods can only be obtained using validated procedures for both uniaxial and multiaxial testing and documentation to establish the mechanisms controlling deformation and fracture for relevant stress states.     

Instability of thermal fracture under the conditions of constrained deformation

We study the processes of quasistatic deformation and fracture of brittle materials under the action of rapidly varying temperature fields. As a fracture criterion, we use the condition of attainment of the critical levels of stresses. The analyses of the stressed state and crack growth are performed under the assumptions that the corresponding elements of the stress field are equal to zero on the newly formed free surfaces and that the conditions of the fracture criterion are satisfied at the ends of the crack. It is shown that the process of crack propagation is unstable for the major part of modes of thermomechanical loading: as soon as the critical stresses are attained at a certain point of the body, the crack instantaneously propagates to a critical size corresponding to a new stable state. It is shown that the mechanical overloading of a specimen can substantially weaken the effect of instability of development of the fracture zone. Examples of fracture of elastic brittle bodies are presented. We also perform the numerical analyses of the processes of initiation and propagation of cracks with regard for the plasticity of the material near its heated surface. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 42, No. 6, pp. 55–60, November–December, 2006.